Methods and systems for controlling motion of and tracking a mechanically unattached probe

ABSTRACT

Methods and systems for controlling motion of and tracking a mechanically unattached magnetic probe are disclosed. One system for controlling motion of mechanically unattached magnetic probe may include a magnetic coil and pole assembly. The magnetic coil and pole assembly includes at least one pole carrier. The pole carrier includes a light transmissive substrate and a plurality of magnetic poles being patterned on the substrate for applying force to a mechanically unattached magnetic probe. A magnetic drive core provides a return path for magnetic flux flowing between the poles. A plurality of magnetic coils are wound around the magnetic drive core for conducting current and applying magnetic force to the probe through the pole pieces. A computer maintains the position of the probe within a volume defined by an optical tracking system by moving the probe and the system under test.

RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.10/786,427 filed Feb. 25, 2004, which claims the benefit of U.S.Provisional Application Ser. No. 60/449,930, filed Feb. 25, 2003, thedisclosures of each of which are incorporated herein by reference intheir entireties.

GOVERNMENT INTEREST

This work was supported by NIH Grant Number 1R01EB000761-01. Thus, theU.S. Government has certain rights to this invention.

TECHNICAL FIELD

The present invention relates to methods and systems for controllingmotion of and tracking a mechanically unattached probe. Moreparticularly, the present invention relates to magnetic structures formagnetically controlling the motion of a mechanically unattached probein one, two, or three dimensions, where the magnetic structures arecompatible with high resolution optics used for imaging and tracking.

BACKGROUND ART

In the field of scanning probe microscopy, small probes interact withsamples under test to measure mechanical properties of the samples undertest. For example, in atomic force microscopy, a small probe (typicallysub-micrometer sized) is attached to the end of a cantilever. As theprobe is scanned across the surface of a sample under test, such as themembrane of a cell, surface irregularities impose a varying force on theprobe, which, in turn, results in a bending or deflection of thecantilever. An optical sensor senses the deflection of the cantileverbased on light reflected from the cantilever and thereby determineschanges in normal position of the probe as it is scanned across thesurface of the sample under test. The changes in normal position of theprobe are used to map the surface of the sample under test.

FIG. 1A illustrates a typical application of atomic force microscopy. InFIG. 1A, a probe 100 is attached to the end of cantilever 102 to map thesurface 104 of a cell membrane. A laser, an optical sensor, and acomputer (not shown) are used to map surface 104 as probe 100 causesdeflections in cantilever 102. One problem with atomic force microscopyis illustrated in FIG. 1B. Atomic force microscopy requires a mechanicalconnection between probe 100 and the remainder of the system viacantilever 102. As a result, conventional atomic force microscopy isunsuitable for measuring mechanical properties of structures withinenclosed regions, such as organelles within a cell membrane, or theother structures that are inaccessible for scanning with a mechanicallyattached probe.

One way to measure properties of structures inside of cells and otherenclosed environments is to mechanically decouple the probe from theremainder of the system. However, once the probe is mechanicallydecoupled from the remainder of the system, tracking and controllingmovement of the probe become problematic. One known technique ofapplying force to a mechanically decoupled probe is referred to as“optical tweezers.” This technique requires high optical fieldintensities that interact strongly with many materials and may produceundesirable side effects on experiments in biological samples.

Commonly-assigned, co-pending international patent application numberPCT/US02/30853 describes a magnetic coil and pole assembly with fourpencil-shaped pole pieces that converge from the vertices of anequilateral tetrahedron. Although such an assembly is useful in manyenvironments, it may be desirable to control the motion of a probe inmicroscopes having high numerical aperture (NA) objective lenses withshort focal distances. For example, some lenses may have numericalapertures greater than or equal to one at focal distances on the orderof millimeters. Such lenses typically have large diameters and thuslimit the space for placement of magnetic pole pieces used to controlthe motion of mechanically unattached probes. The space for placing polepieces is even further limited when high NA objective lenses are placedboth above and below the sample under test. In addition, at somepositions within the volume defined by the pole pieces in a four-polesystem, moving the probe in certain directions can be difficult.

Another factor to be considered in designing and placing magnetic polepieces to control motion of a mechanically unattached magnetic probe isthat the magnetic force on the probe for a given magnetic field variesinversely with r⁵, where r is the distance from the pole tip applyingthe magnetic force to the magnetic probe. Thus, in order to apply strongmagnetic forces to a probe, it is desirable that the pole tips be keptas close as possible to the probe. However, because the pole tipscompete for space with imaging and tracking optics, designing a systemthat achieves desired magnetic forces and that is compatible withhigh-resolution optics is difficult.

Accordingly, there exists a long felt need for improved magneticstructures for applying magnetic force to a mechanically unattachedprobe that are suitable for use with high resolution optics or in otherspace-constrained environments.

DISCLOSURE OF THE INVENTION

The present invention includes methods and systems for controlling andtracking the motion of a mechanically unattached probe. By mechanicallyunattached, it is meant that the probe is not mechanically attached toits motion control system. The present invention is not limited tocontrolling the motion of a probe that is not mechanically attached toanything. For example, a probe may be weakly bound to a surface of asample under test and be allowed to diffuse on the surface. In anotherexample, a probe may be bound to the surface of a sample under test andforces may be applied to the probe in a direction normal to the surfaceto measure the forces that bind the probe.

According to one aspect of the invention, a magnetic coil and poleassembly for controlling motion of a mechanically unattached probe isprovided. The assembly includes at least one magnetic pole carrier. Thepole carrier includes a light transmissive substrate and a plurality ofmagnetic pole pieces being patterned on the substrate in a manner forapplying force to a mechanically unattached magnetic probe. A magneticdrive core is magnetically coupled to the magnetic poles to provide alow reluctance return path for the magnetic flux induced between thepoles. A plurality of magnetic coils is wound around the drive core forconducting current and applying magnetic force to the probe.

In one implementation, the magnetic pole carrier comprises a slide coverslip and the magnetic poles are thin film structures patterned on thecover slip. Using a slide cover slip is advantageous because it is thinand light transmissive. Using thin film magnetic poles is alsoadvantageous due to the thinness of the poles and the ability tofabricate the poles using semiconductor manufacturing processes.However, the present invention is not limited to using a slide coverslip for the pole plate or using thin film magnetic poles. Any lighttransmissive substrate and pole structure suitable for use with highnumeral aperture lenses in an optical microscope are intended to bewithin the scope of the invention. For example, in an alternateimplementation, the pole pieces may be laminated foil structures cutfrom a sheet of magnetic material rather than thin film structuresmanufactured using semiconductor manufacturing techniques.

If three dimensional motion control is desired, a hexapole pole piecearrangement may be used for the magnetic coil and pole assembly. Inalternate arrangements, thin film magnetic poles may be formed inarbitrary patterns on a substrate to apply desired magnetic forces toone or more mechanically unattached magnetic probes in one, two, orthree dimensions. For example, if motion in a single direction isdesired, a magnetic pole and coil assembly of the present invention mayinclude a single thin film or thin foil pole piece located on a lighttransmissive substrate. Locating any number of pole pieces on a lighttransmissive substrate is intended to be within the scope of theinvention.

Accordingly, it is an object of the invention to provide magneticstructures for controlling motion of a mechanically unattached magneticprobe.

It is another object of the invention to provide a magnetic coil andpole assembly for controlling motion of a mechanically unattachedmagnetic probe and that is suitable for use with high numerical aperturelenses.

Some of the objects of the invention having been stated hereinabove, andwhich are addressed in whole or in part by the present invention, otherobjects will become evident as the description proceeds when taken inconnection with the accompanying drawings as best described hereinbelow.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the invention will now be explained withreference to the accompanying drawings of which:

FIGS. 1A and 1B are sectional views of a biological cell and a probeassociated with conventional atomic force microscopy techniques;

FIG. 2 is a block diagram of a three-dimensional force microscopeinstrument including a magnetic coil and pole assembly according to anembodiment of the present invention;

FIGS. 3A and 3B are schematic diagrams illustrating exemplary lenseshaving different numerical apertures;

FIG. 4A is a perspective view of a cube illustrating exemplary poleplacements for a hexapole design according to an embodiment of thepresent invention;

FIG. 4B is a plan view of triangles 402 and 404 viewed along line 406illustrated in FIG. 4A;

FIG. 4C is a perspective view of a hexapole arrangement for magneticpole pieces according to an embodiment of the present invention;

FIG. 5A is a perspective view of a magnetic pole and coil assemblyaccording to an embodiment of the present invention;

FIG. 5B is a side view of a pole piece, upper and lower pole carriers,and portions of upper and lower drive ring cores according to anembodiment of the present invention;

FIG. 6 is a perspective view of a magnetic drive ring core according toan embodiment of the present invention;

FIG. 7 is a top view of a magnetic drive ring core with magnetic coilsbeing wound around the core according to an embodiment of the presentinvention;

FIG. 8 is a top view of a lower pole carrier patterned with thin filmmagnetic pole pieces according to an embodiment of the presentinvention;

FIG. 9 is a top view of a lower pole carrier and a lower magnetic drivering core according to an embodiment of the present invention;

FIG. 10 is a top view of an upper magnetic drive ring core and upperpole carrier according to an embodiment of the present invention;

FIG. 11 is a top view of upper and lower magnetic cores and upper andlower magnetic pole carriers according to an embodiment of the presentinvention;

FIG. 12 is a side view of a magnetic coil and pole assembly and upperand lower objective lenses according to an embodiment of the presentinvention;

FIG. 13 is a top view illustrating exemplary magnetic forces that may beused to pull a probe towards one pole piece in a hexapole arrangementaccording to an embodiment of the present invention;

FIG. 14A is a top view of a pole carrier including peaked magnetic polepieces according to an embodiment of the present invention;

FIG. 14B is a close-up view of the pole carrier with peaked magneticpole pieces illustrated in FIG. 14A;

FIG. 15A is an optical schematic diagram illustrating exemplary imagingoptics suitable for imaging a mechanically unattached magnetic probeaccording to an embodiment of the present invention;

FIG. 15B is a top view illustrating magnetic pole pieces as viewedthrough an objective lens;

FIG. 16 is an optical schematic diagram illustrating exemplary trackingoptics suitable for tracking motion of a mechanically unattachedmagnetic probe according to an embodiment of the present invention;

FIG. 17 is a perspective view illustrating exemplary coordinates andangles used in equations for tracking a mechanically unattached magneticprobe in three-dimensions according to an embodiment of the presentinvention;

FIG. 18A is a graph of a linear profile of a normalized Z displacementsignal generated by a system for tracking a mechanically unattachedmagnetic probe in three dimensions according to an embodiment of thepresent invention; and

FIG. 18B is a graph of a linear profile of a normalized X displacementsignal generated by a system for tracking a mechanically unattachedmagnetic probe in three dimensions according to an embodiment of thepresent invention.

DETAILED DESCRIPTION OF THE INVENTION

The methods and systems for controlling motion of and tracking amechanically unattached magnetic probe may be implemented in 3D forcemicroscopes with high numerical aperture lenses. FIG. 2 is a blockdiagram of an exemplary 3D force microscope in which a magnetic coil andpole assembly of the present invention may be used. Referring to FIG. 2,the system includes magnetic coil and pole assembly 200 for controllingthe force applied to a mechanically unattached magnetic probe 202. Themagnetic force supplied by assembly 200 is controlled by a computer 204.More particularly, D/A board 210 converts the digital coil controlsignal output from computer 204 into analog format. Power amplifiers 212amplify the signal voltages output from D/A board 210 and output theamplified signals to magnetic coil and pole assembly 200 as polemagnetizing currents. Magnetic coil and pole assembly 200 transduces thepole magnetizing currents to magnetomotive forces which induce amagnetic field that is coupled to probe 202, thereby generating amagnetic force on probe 202.

The system also includes a piezoelectric (x, y, z) translation stage 206controlling position of sample under test (SUT) 205, which physicallycontains probe 202. The motion of SUT 205 is coupled to probe 202 by theviscoelastic properties of SUT 205, thereby also affecting the motion ofprobe 202. A position control feedback loop comprises position gauge230, PID controller 232, and high voltage driver 234 in controllermodule 208; and piezoelectric actuators 226 and capacitive positionsensors 228 in translation stage 206. This feedback loop is used torapidly and accurately cause the position of SUT 205 to follow aposition control signal from computer 204, and to feed back a stageposition signal to computer 204 representing the measured position ofSUT 205.

In order to image and track probe 202, the system illustrated in FIG. 2includes various optical components. These components may include laser214, optics 216, and optics 218. Laser 214 generates light to bescattered from probe 202 and used to track probe 202. Optics 216includes a series of lenses used for both tracking and imaging. Optics218 collect light scattered by probe 202, light scattered by the samplebeing monitored, and light transmitted directly from laser 214. Aquadrant photodiode 220 (QPD) converts the light collected by optics 218into electronic signals used to determine the position of probe 202.Transimpedance amplifiers 222 convert the currents output by QPD 220into voltages indicative of probe position. An A/D board 224 convertsthe voltages output from transimpedance amplifiers 222 into digitalsignals indicative of probe position. Computer 204 executes codes, whichtransform the probe position signals from A/D board 224 into estimatesof the (x, y, z) position of probe 202 relative to the center of thebeam waist of laser 214 at the focus of optics 216. The functional rangeof this method is limited to a radius of approximately one wavelength ofthe light of laser 214 from the center of the beam waist.

Maintaining the probe within this functional range is essential to thevarious operational modes. In all modes, the feedback minimizes theestimated (x, y, z) position of probe 202 relative to the center of thebeam waist of laser 214 at the focus of optics 216.

One mode in which the system illustrated in FIG. 2 may be operated isposition control mode. In position control mode, computer 204 provides adesired position control signal to cause the position of SUT 205 tofollow a predetermined trajectory. Computer 204 also executes feedbackcode driving the force control signal to cause probe 202 to remain fixedrelative to the beam waist. This is equivalent to causing probe 202 tomove relative to SUT 205 in a trajectory that is exactly opposite thepredetermined trajectory of SUT 205. The force control signal representsthe forces applied to probe 202 to cause it to follow this trajectory.This mode is useful for measuring viscoelastic properties such as fluidviscosity in SUT 205.

Another mode is force control mode. In force control mode, computer 204provides a desired force control signal to apply a predetermined forceprofile to probe 202 over time. Computer 204 also executes feedback codedriving the position control signal to cause probe 202 to remain fixedrelative to the beam waist. This is equivalent to causing probe 202 tomove relative to SUT 205 in a trajectory that is exactly opposite themotion caused by the position control signal. The position controlsignal represents the trajectory followed by probe 202 in response tothe applied force signal.

A mode closely related to position control mode is velocity controlmode. In velocity control mode, Computer 204 calculates a positiontrajectory satisfying initial conditions and a predetermined desiredvelocity profile, and uses position control mode to cause probe 202 tofollow this position trajectory.

The present invention is not limited to these operational modes. Anycombination of feedback from stage position and probe position signalsto force control and position control signals is intended to be withinthe scope of the invention. In addition, the present invention is notlimited to using the forward light scattering method described withrespect to FIG. 2 to measure probe position. In an alternateimplementation, video imaging may be used to track the position of probe202 without departing from the scope of the invention. Using videoimaging may provide further operational modes.

High NA Lenses

As stated above, the present invention preferably includes magneticstructures that are suitable for use with high numerical apertureobjective lenses. FIGS. 3A and 3B illustrate lenses with differentnumerical apertures. In FIG. 3A, a lens 300 is spaced from a sampleunder test 302 by the focal distance of lens 300. The angle ax, which isone half of the angle from the sample to the outside edges of lens 300,determines the numerical aperture. Assuming that the medium between lens300 and sample 302 has an optical index of refraction η, the numericalaperture is equal to ηsin((α). In FIG. 3B, another lens 304 has a largerdiameter and shorter focal length than lens 300. As a result, the angleα and hence the numerical aperture of lens 304 is larger than that oflens 300. As the diameter of a lens increases and the focal lengthdecreases, the numerical aperture approaches one. For lenses with anumerical aperture of one or greater, the space for placing magneticpole pieces is limited. Accordingly, the present invention preferablyincludes pole piece structures that are capable of controlling motion ofa magnetic probe near high numerical aperture lenses or in otherspace-constrained environments.

Hexapole Geometry for Magnetic Coil and Pole Assembly

In some applications, it may be desirable to control the motion of amechanically unattached probe in any direction in three dimensions. Onedesign for magnetic coil and pole assembly 200 that is suitable forthree dimensional motion control is a hexapole design. In the hexapoledesign, six thin film or laminated foil poles are used to control themotion of a mechanically unattached probe in three dimensions. FIG. 4Aillustrates the concept behind pole placement for the hexapole design.In FIG. 4A, if a sample under test is placed at the center of a cube400, the sample is equidistant from the midpoints of each face of cube400. In addition, the lines that connect the midpoints of opposite facesof cube 400 are orthogonal to each other. These lines form a Cartesiancoordinate system. Thus, the midpoints of the faces are ideal locationsfor placement of the magnetic pole tips.

If the midpoints of adjacent faces of cube 400 are connected as shown inFIG. 4A, two equilateral triangles 402 and 404 are formed. Theequilateral triangles are parallel to each other and are rotated withrespect to each other by 60°. FIG. 4B illustrates triangles 402 and 404looking along dashed line 406 shown in FIG. 4A. In FIG. 4B, it can beseen that the vertices of triangles 402 and 404 are equidistant from thecenter of cube 400 in FIG. 4A. In addition, triangles 402 and 404 definea cylindrical working volume 408 between them. This working volumerepresents the area in which motion of probe 202 can be controlled inthree dimensions. However, the present invention is not limited tocontrolling the motion of probe 202 in cylindrical working volume 408.For instance, it may be desirable to apply increased force on the probeat the expense of force symmetry. In such an instance, the sample may beplaced near one of the pole tips for increased magnetic force.

FIG. 4C illustrates the result of placing thin film or laminated foilmagnetic pole pieces with pole tips located at the vertices of triangles402 and 404 illustrated in FIGS. 4A and 4B. In FIG. 4C, pole pieces 410lie in a common plane with pole tips corresponding to vertices oftriangle 402. Similarly, pole pieces 412 lie in a common plane with poletips corresponding to vertices of triangle 404. Pole pieces 410 arerotated by an angle of 60° with regard to pole pieces 412. Like theplanes that contain triangles 402 and 404, the plane that contains polepieces 410 is parallel to the plane that contains pole pieces 412.

In one exemplary implementation, the hexapole design may be implementedby providing pole pieces 410 and 412 on upper and lower carriers andproviding pairs of magnetizing coils for magnetizing each pole piece.FIG. 5A is a perspective view of magnetic pole and coil assembly 200where the assembly includes a hexapole geometry as illustrated in FIG.4C. Referring to FIG. 5A, assembly 200 includes an upper pole carrier500 and a lower pole carrier 502. Upper pole carrier 500 includes polepieces 410located on an upper surface thereof. Lower pole carrier 502includes pole pieces 412 located on a lower surface thereof.

In order to apply magnetic force to a mechanically unattached probe,assembly 200 includes upper and lower magnetic coil assemblies 504 and506. Assemblies 504 and 506 each include a plurality of magnetic coils508 being wound around tabs 510 on upper and lower magnetic drive ringcores 512A and 512B. Assembly 200 may also include a mounting stage 514for holding the cores, coils, carriers, and the sample. In theillustrated example, mounting stage 514 includes a hinged portion 516for holding upper magnetic coil assembly 504. In operation, hingedportion 516 is closed to bring assembly 504 in close proximity to thepole pieces located on upper pole carrier 502.

The surface of each tab 510 that faces one of the pole pieces 410 or 412is referred to as a pole face. When hinged portion 516 is closed, theremay be air gaps between the pole faces and the pole piece that each poleface pair is magnetizing. FIG. 5B illustrates this concept. Referring toFIG. 5B, coils 508 and associated tabs 510 are located on opposite sidesof pole piece 410. The distance between the lower face of uppertab 510and pole piece 410 is illustrated as h₁. The distance between lower tab510 and pole piece 410 is illustrated by h₂. In order to ensure a lowreluctance path for flux emanating from tabs 510 to pole piece 410, itis preferable that the distances h₁ and h₂ be much less than the crosssectional area formed by the intersection of the pole faces formed bytabs 510 and pole piece 410. For example, the cross sectional areaformed by the intersection of the pole face and pole piece 410 ispreferably at least one order of magnitude and even more preferably atleast two orders of magnitude greater than h₁ and h₂. Providing a largecross sectional area relative to h₁ and h₂ compensates for the increasein reluctance caused by the air gap and glass material between the polefaces and pole piece 410.

FIG. 6 is a perspective view of magnetic drive ring core 512A or 512Baccording to an embodiment of the present invention. Magnetic drive ringcore 512A is preferably identical in structure to magnetic drive ringcore 512B. Referring to FIG. 6, magnetic drive ring core 512A or 512Bincludes tabs 510 around which coils 508 may be wound. Drive ring core510 is preferably made of a material with resistance to eddy currents,hysteresis, and magnetostriction, yet with high permeability. Suchcharacteristics allow a large flux to be generated, while minimizinglosses due to eddy currents. One material suitable for forming drivering core 512A or 512B is tape wound laminated metglass. Tabs 510 arepreferably equally spaced around core 512A or 512B.

FIG. 7 is a top view illustrating coils 508 wound around tabs 510 ofcore 512A or 512B. In FIG. 7, each coil is formed of a single layerspiral of flat magnetic wire. Coils 508 form an aperture 700 suitablefor placement of high resolution optics. For the hexapole geometry,there are preferably six coils on each drive ring—an upper coil and alower coil for each pole piece.

FIG. 8 is a top view of lower pole carrier 502 including lower polepieces 412. In FIG. 8, lower pole pieces 412 are on the underside ofpole carrier 502. In one exemplary implementation, magnetic thin filmsmay be photolithographically patterned on glass substrates and thenelectroplated with permalloy to form pole plates. That is, pole pieces410 and 412 may be patterned on glass carriers 500 and 502 to form upperand lower pole plates. In an alternate manufacturing method, pole pieces410 and 412 may be patterned on glass carriers 500 and 502 by cuttingthe appropriate shapes from thin sheets of permalloy foil and thenlaminating the pole pieces onto carriers 500 and 502. Each pole platemay include three poles in the hexapole arrangement. As illustrated inFIG. 5A, the two pole plates make up the six poles of the hexapolegeometry. The upper and lower pole carriers may be identicallypatterned. However, since one pole plate is flipped relative to theother pole plate, it is oriented with a rotation of 60° with respect tothe other pole plate.

The present invention is not limited to using glass for pole carriers500 and 502. Any material that is transmissive to electromagnetic energyat the wavelengths used for imaging and/or tracking is intended to bewithin the scope of the invention. The present invention is likewise notlimited to using permalloy for pole pieces 410 and 412. Any suitablemagnetic material with low hysteresis, low eddy currents, highsaturation flux, and high permeability may be used without departingfrom the scope of the invention.

The thicknesses of pole pieces 410 and 412 may be selected based on avariety of engineering trade-offs. For example, in a configuration inwhich pole pieces 410 and 412 are sandwiched between upper and lowerhigh NA objective lenses, the focal distances of the lenses, the spacerequired for the sample slide, and the space required for pole carriers500 and 502 limit the thicknesses of pole pieces 410 and 412. Polepieces 410 and 412 are preferably made thick enough so that they do notsaturate with magnetic flux before the flux reaches the pole tips. In ahigh force application where increased magnetic force is more importantthan three dimensional motion control symmetry, pole pieces 410 and 412can be made thicker and located in the same plane.

FIG. 9 is a top view of lower pole carrier 502 mounted on lower drivering core 512B. For simplicity of illustration, coils 508 are not shown.In FIG. 9, each pole piece 412 is patterned on the surface of polecarrier 502 that faces the pole faces of tabs 510. The remaining tabs oflower drive ring core 512B are used to magnetize pole pieces 410 ofupper pole carrier 500 (not shown in FIG. 9).

FIG. 10 is a top view of upper magnetic drive ring core 512A. In FIG.10, tabs 510 are located on the lower surface of core 512A. Pole pieces412 are patterned on the surface of pole carrier 500 that faces thecorresponding pole faces of tabs 510. The remaining tabs 510 are used tomagnetize coils 412 on lower pole carrier 502. In the configurationillustrated in FIG. 11, each pole piece 410 and 412 is sandwichedbetween two tabs 510 to provide a low reluctance path for magnetic flux.

FIG. 11 is a top view of upper and lower magnetic pole carriers 500 and502 and upper and lower drive ring cores 512A and 512B in a sandwichedconfiguration. It can be seen from FIG. 11 that when pole carrier 500 isplaced on top of pole carrier 502, pole pieces 410 and 412 form thehexapole geometry. Although not illustrated in FIG. 11, a specimen slidemay be placed between upper and lower pole carriers 500 and 502. Thespecimen slide may include a mechanically unattached probe located in anaqueous medium so that magnetic force can be applied on the probe usingpole pieces 410 and 412.

FIG. 12 is a side view of magnetic coil and pole assembly located in aspace-constrained environment with high NA lenses on opposite sides ofthe assembly according to an embodiment of the present invention.Referring to FIG. 12, upper and lower pole carriers 500 and 502 arelocated on opposite sides of sample plate 518. It can be seen that dueto the compact configuration of the upper and lower pole carriers, alens 1200, which may be a high numerical aperture lens (NA≧1), may beplaced in close proximity to the sample. Another lens 1202, which mayalso be a high NA lens, may be placed above assembly 200. In analternate configuration, either lens may be replaced by a lower NA lens(NA<1) without departing from the scope of the invention. The gapsbetween lenses 1200 and 1202 and the respective pole carriers may befilled with a predetermined material to increase the numerical apertureof the lenses. In one example, the predetermined material may be water.The sample under test may be imaged through lower pole carrier 502. Thetracking laser may also pass through lower objective lens 1200, lowerpole plate 502, upper pole plate 500, and into lens 1202.

In order to drive one of the pole pieces 410 or 412, it is desirable tomagnetize the upper and lower coils 508 above and below the pole piecebeing magnetized so that each coil has the same magnetic sense in thedirection of the pole piece. That is, the upper and lower coils for aparticular pole piece are preferably magnetized so that the north polesor the south poles of the coils face each other. This may beaccomplished by wiring coils in the same vertical stack in series andwinding the coils in opposite directions so that a current flowing in agiven direction in each coil pair results in either the north or southpoles facing each other.

Magnetizing the coils so that like poles face each other directsmagnetic flux in the direction of the pole tip of the pole piece andinto the sample. The flux may return through the other pole tips and thedrive ring cores. It should be noted that it is not desirable tomagnetize coils in the same vertical stack so that unlike poles faceeach other. For example, if a north pole in a vertical coil stack facesa south pole, flux emanating from the north pole will terminate in thesouth pole, rather than flowing through the pole piece. This isundesirable since less flux will reach the magnetic probe.

In order to effect motion towards one of the pole pieces, the pole piecemay be energized with a magnetic force that is stronger in magnitudethan the magnetic force of the other pole pieces. In addition, themagnetic sense of the pole piece towards which motion is desired ispreferably opposite that of the other pole pieces. FIG. 13 illustratesthis concept. Referring to FIG. 13, one pole piece 412 is preferablymagnetized with a magnetizing force of 5N, indicating a strong magneticforce with a north magnetic sense. The remaining pole pieces arepreferably magnetized with weak south fields S, where S represents afield that is equal in magnitude to N. Probe 202 will travel in thedirection of increasing magnetic flux. In FIG. 13, the probe will travelin the direction of the 5N pole piece. By utilizing differentmagnetizing currents and the geometry illustrated in FIG. 5A, motion ofprobe 202 in three dimensions can be achieved.

Alternate Pole Piece Geometries

Although the examples described above with regard to FIGS. 4A through 13illustrate a hexapole design, the present invention is not limited tousing a hexapole design. Forming any thin film or thin foil pole piecestructure on a pole carrier to achieve a desired magnetic force on oneor more mechanically unattached probes is intended to be within thescope of the invention. FIG. 14A is a top view of a pole carrier 1400with an alternate pole piece configuration. FIG. 14B is a close-up viewof the pole pieces and pole carrier illustrated in FIG. 14A. In FIGS.14A and 14B, pole carrier 1400 may be a glass substrate, as describedabove. In FIG. 14, pole carrier 1400 includes pole pieces 1402 and 1404.Pole pieces 1402 and 1404 may be thin films or thin foils formed in apeaked or sawtooth pattern to form a plurality of opposing pole tips1406 for applying forces over a wide area of a sample. Pole pieces 1402and 1404 may be coupled to coil and pole assembly 200 at locationsindicated by dotted lines in FIG. 14A. Pole tips 1406 may be magnetizedin any suitable manner to apply force to a plurality of mechanicallyunattached probes. For example, pole tips 1406 on pole piece 1402 may beinitially magnetized to have a north magnetic sense and pole tips 1406on pole piece 1404 may be initially magnetized to have a south magneticsense. A plurality of magnetic probes may be placed between the poletips in the sample under test. The magnetic polarity of the pole tipsmay be alternated over time and the force response of the sample undertest may be measured over a period of time.

Imaging Optics

As discussed above, the present invention may include imaging optics forviewing probe 202 in the sample under test. FIG. 15A is an opticalschematic diagram of exemplary imaging optics suitable for use with themethods and systems of the present invention. Referring to FIG. 15A, theimaging optics include a light source 1500 for illuminating the objectbeing imaged. Light source 1500 may be any suitable light source capableof uniform illumination of an object. In a preferred embodiment, lightsource 1500 is a fiber light consisting of a halogen lamp and a bundleof optical fibers with the output coupled to the lower end of theimaging optics. An exemplary commercially available light sourcesuitable for use with the present invention is the M1000 Fiber Lightavailable from Edmond Optics.

In a preferred embodiment of the invention, Koehler illumination is usedto illuminate the subject. In Koehler illumination, light from the lightsource is focused by a collector lens to form an image of the lightsource on the back focal plane of a condenser. Accordingly, in FIG. 15A,collector lenses 1502 form an image of light source 1500 on the backfocal plane of a condenser 1200. Condenser 1200 is an objective lensthat corrects for spherical aberration, coma, and chromatic aberrationand is optimized for bright field illumination. Probe 202 being imagedis located at the focal point of condenser 1200 in a sample chamber1504. Upper objective lens 1202 forms an image. A tube lens 1506 focusesthe lights rays exiting objective 1202 onto the image plane of a CCDcamera 1510. A filter 1508 filters the light entering CCD camera 1512.CCD camera 1510 converts the incident photons into an electronic signaland produces an electronic image of probe 202 and the sample under test.

The imaging system illustrated in FIG. 15A is referred to as a brightfield imaging system. However, the present invention is not limited tousing bright field imaging. For example, in an alternate embodiment ofthe invention, fluorescent imaging can be used to produce electronicimages of probe 202 and the sample under test.

One problem with any magnetic pole and core assembly in which the polepieces intrude in the optical path is that the pole pieces may adverselyaffect imaging and tracking because the pole pieces block light raysthat would otherwise be collected by the objective lenses. FIG. 15Billustrates this concept. FIG. 15B is a schematic diagram illustratingan exemplary view of the system as seen through upper objective lens1202. In FIG. 15B, upper pole pieces 410 appear as fuzzy opaque regionsin the scene because they are out of focus. Lower pole pieces 412 alsoappear as out of focus images, since they are outside the focal lengthof objective lens 1202. In order to compensate for the effect of polepieces 410 and 412 on imaging and tracking, the optical signal exitinglenses 1200 and 1202 can be post processed using a filter function toaccount for any distortion caused by the pole pieces. The filterfunction may be the inverse of the transfer function caused by theinterference of pole pieces 410 and 412 on incident light. Such atransfer function may be experimentally determined and programmed intocomputer 204 illustrated in FIG. 2.

Tracking Optics

In order to control the position of a mechanically unattached probe inthree dimensions, it is necessary to be able to track the probe in threedimensions. Additional reasons for and advantages of tracking the probein three dimensions are that such tracking allows mapping of surfaceswithin a tracked volume, and when coupled with applied forcemeasurements, viscoelastic properties of samples under test can bedetermined. For example, three-dimensional optical tracking whileapplying forces in three dimensions can be used to determine mechanicalproperties of structures within a cell, within a cell culture, or in anyother biological sample. Selective binding of the probe to specificorganelles and large macromolecules can be used to determine bindingcoefficients.

FIG. 16 illustrates exemplary tracking optics that may be used in asystem for three dimensional tracking and position control of a freefloating probe according to an embodiment of the present invention. InFIG. 16, the tracking optics include a laser light source 214 coupled tothe remainder of the optics via a single mode optical fiber 1600. Acollimating lens 1602 collimates the diverging light rays exiting fiber1600. Condensing lens 1200 converges the light rays on the specimensample 518. Objective lens 1202 collects the transmitted light beam andthe light scattered from the probe on its back focal plane where itinterferometrically forms the Fourier transform of the superposition ofthese two light fields. Lens 1604 reprojects the optical Fouriertransform of the sample from the back focal plane of objective lens 1202to quadrant photodiode 220. Quadrant photodiode 220 converts the lightinto electronic signals indicative of optical intensities at variouspositions on the surface of quadrant photodiode 220.

Optical Tracking Theory and Equations

Optical tracking equations based on intensity measurements made byquadrant photodiode 220 are theoretically based on Maxwell's WaveEquations. The following assumptions were made in order to perform theoptical tracking calculations:

-   -   1. The probe acts like a Rayleigh scatterer (a dielectric sphere        with a radius smaller than the wavelength of the incident        light).    -   2. The finite size of the particle is accounted for, with a        dielectric constant, ε, and a polarizability, α,        $\alpha = {a^{3}{\eta_{solvent}^{2} \cdot \frac{( {m^{2} - 1} )}{( {m^{2} + 2} )}}}$        Where $m = \frac{\eta_{probe}}{\eta_{solvent}}$    -   and η_(probe) and η_(solvent) are the refractive indices of the        probe and the solvent in which the probe is floating, and a is        the radius of the probe. To simplify the math, the probe        position r′ is described in cylindrical coordinates z′,        ρ′²=x′²+y′², φ=atan(y′/x′), while the detected interference at        point r is described in spherical coordinates (r, ν, φ) around        the optical axis. FIG. 17 illustrates the spherical and        cylindrical coordinates used in the probe position calculations.    -   3. The propagating electromagnetic field generated by the laser        is modeled as a Gaussian beam with a scalar wavenumber k        k=|k|=2πη_(solvent)/λ    -   the radius of curvature of the Gaussian beam is        ${R(z)} = {z\lbrack {1 + ( \frac{z_{0}}{z} )^{2}} \rbrack}$    -   the beam waist radius in the focal plane is        $\omega_{0} = \sqrt{\lambda\quad\frac{z_{0}}{\pi}}$    -   and the phase is        ${\zeta(z)} = {a\quad{{\tan( \frac{z}{z_{0}} )}.}}$

At the focus (i.e., the sample under test), the field generated by laser214 undergoes the Gouy-phase jump, resulting in a ninety-degree phaseshift between the focused laser field and a simple plane wavedescription of the phase of the light. The complex amplitude of theincident Gaussian electromagnetic field on the probe is given by$\begin{matrix}{{E_{i}(r)} = {E_{0}\frac{w_{0}}{w(z)}{\exp\lbrack {- \frac{\rho^{2}}{w^{2}(z)}} \rbrack}{\exp\lbrack {{{- {\mathbb{i}}}\quad{kz}} - {{\mathbb{i}}\quad k\quad\frac{\rho^{2}}{2{R^{2}(z)}}} + {{\mathbb{i}}\quad{\zeta(z)}}} \rbrack}}} & (1)\end{matrix}$

When the field at quadrant photodiode 220 is observed, far from thefocal plane (r>>z₀), the following approximations can be used:${{\zeta(z)} = {{\arctan( \frac{z}{z_{0}} )} \approx \frac{\pi}{2}}},{z \approx r},{{R(z)} \approx \infty}$${{\omega(z)} \approx \frac{\omega_{0}z}{z_{0}}},{{\sin(\upsilon)} \approx \upsilon},{\rho < \omega_{0}},{{\exp( {- \frac{\rho^{2}}{{\omega(z)}^{2}}} )} \approx 1}$the unscattered light in the far field is then given by $\begin{matrix}{{{E_{u}(r)} = {{\mathbb{i}}\quad E_{0}\frac{k\quad\omega_{0}}{2r}{\exp\lbrack {{{\mathbb{i}}\quad{kr}} - {\frac{1}{4}k^{2}\omega_{0}^{2}\upsilon^{2}}} \rbrack}}},} & (2)\end{matrix}$and this is normalized by${E_{0} = \frac{2}{( {\omega_{0}\sqrt{{\pi ɛ}_{S}c_{S}}} )}},$where c_(s) is the speed of light in the sample under test. When a probewith a polarizability α, is placed at a position r′, near the geometricfocal point, the Rayleigh approximation for the scattered field at larger>>z₀ is $\begin{matrix}{{E_{S}( {r,r^{\prime}} )} \approx {\frac{k^{2}\alpha}{r}{E( r^{\prime} )}{\exp\lbrack {{\mathbb{i}}\quad k{{r - r^{\prime}}}} \rbrack}}} & (3)\end{matrix}$The change in the average light intensity I, due to the interferencebetween the incident laser beam and the scattered light (subtracting theoffset |E|²) is${\delta\quad I} = {{\frac{ɛ_{S}c_{S}}{2}( {{{E + E^{\prime}}}^{2} - {E}^{2}} )} \approx {ɛ_{S}c_{S}{{Re}( {EE}^{\prime} )}}}$Using equations (2) and (3), the intensity change in the back focalplane of objective 1202 for a probe displacement r′, from thegeometrical focal point of objective 1202 is $\begin{matrix}{{\frac{\delta\quad{I( {r,r^{\prime}} )}}{I_{tot}} = {{J( {r,r^{\prime}} )}\sin\quad\text{[}{k( {r - {{r - r^{\prime}}} - z^{\prime} - \frac{\rho^{\prime 2}}{2{R( z^{\prime} )}} + \frac{\zeta( z^{\prime} )}{k}} \rbrack}}}{Where}{{J( {r,r^{\prime}} )} = {\frac{2k^{3}\alpha}{\pi\quad r^{3}}( {1 + ( {z^{\prime}/z_{0}} )^{2}} )^{{- 1}/2}{\exp\quad\lbrack {{- \frac{\rho^{\prime 2}}{{\omega( z^{\prime} )}^{2}}} - {k^{2}\omega_{0}^{2}\vartheta^{2}}} \rbrack}}}} & (4)\end{matrix}$The z-signal is extracted from the total intensity at the back focalplane of lens 1202. Thus, equation (4) can be integrated over all anglesto obtain the z-signal along the optical axis as: $\begin{matrix}{{\frac{I_{z}}{I}( z^{\prime} )} = {\frac{8\quad k\quad\alpha}{{\pi\omega}_{0}^{2}}( {1 + ( {z^{\prime}/z_{0}} )^{2}} )^{{- 1}/2}\sin\quad( {\arctan\quad( \frac{z^{\prime}}{z_{0}} )} )}} & (5)\end{matrix}$

FIG. 18A is a graph of normalized intensity versus probe displacement inthe Z direction (perpendicular to the surface of quadrant photodiode220). The graph was generated assuming a 650 nm laser, a beam waistradius of 700 nm, a probe radius a=300 nm, and the refractive indices ofthe probe and the sample under test at 1.5 and 1.33, respectively. Theresult illustrated in Equation 5 and FIG. 18A is intuitive—as probemoves towards quadrant photodiode 220 in the Z direction, the normalizedintensity increases and as the probe moves away from quadrant photodiode220, the normalized intensity decreases. Thus, the change in intensityof the scattered and directly transmitted light measured by quadrantphotodiode 220 can be used to track motion of probe 202 in the Zdirection.

The lateral probe displacement (i.e., displacement in a plane parallelto the surface of QPD 220), may be determined by the difference inintensity between two halves of QPD 220. Thus, it is necessary tointegrate half of the detection area to obtain the lateral signals. Thetwo-dimensional result for a probe displacement, p′, in the focal planeat an angle φ′ is $\begin{matrix}{{\frac{I_{x}}{I}( {p^{\prime},\varphi^{\prime}} )} = {\frac{16k\quad\alpha}{\sqrt{{\pi\omega}_{0}^{2}}}\cos\quad( \varphi^{\prime} )( \frac{\rho^{\prime}}{\omega_{0}} )\exp\quad( {- ( \frac{\rho^{\prime}}{\omega_{0}} )^{2}} )}} & (6)\end{matrix}$

FIG. 18B is a graph of normalized intensity versus displacement in the Xdirection generated by assuming the same laser, beam waist, beam radius,and probe and sample materials described above with regard to FIG. 18A.As illustrated in FIG. 18B, normalized intensity is zero fordisplacements to the far left and the far right of the center ofquadrant photodiode 220. This is because light is being scatteredoutside of the image plane of quadrant photodiode 220. In the regionnear the center of quadrant photodiode 220, normalized intensity variesapproximately sinusoidally with displacement. The results fordisplacement in the Y direction are similar to those illustrated in FIG.18B for the X direction. Thus, by measuring the intensity andcalculating the change in intensity of light measured by differentregions of quadrant photodiode 220, motion of a mechanically unattachedprobe can be tracked in a plane parallel to the surface of quadrantphotodiode 220.

Equations (5) and (6) or approximations of Equations (5) and (6) may beimplemented as a position calculator in hardware and/or software incomputer 204 illustrated in FIG. 2. Such a position calculator receivesthe signals output from quadrant photodiode 220 and calculates position,velocity, and/or acceleration of probe 202 in the sample under test.

Thus, the present invention includes methods and systems for controllingmotion of and tracking a mechanically unattached probe. In oneimplementation, the invention includes a magnetic pole and coil assemblysuitable for use in space-constrained environments, such as opticalmicroscopes with high numerical aperture lenses. In order to effectmotion of a mechanically unattached probe in three dimensions, upper andlower pole carriers may be patterned with a plurality of pole pieces.Upper and lower magnetic drive ring cores include coils that magnetizethe pole pieces to apply magnetic force to the probe. The pole piecesmay be manufactured using any suitable manufacturing technique formaking thin magnetic materials in predetermined patterns. Examples offabrication techniques include any semiconductor fabrication techniquesor-cutting the pole piece patterns from thin foils.

It will be understood that various details of the invention may bechanged without departing from the scope of the invention. Furthermore,the foregoing description is for the purpose of illustration only, andnot for the purpose of limitation, as the invention is defined by theclaims as set forth hereinafter.

1. A system for controlling motion of and optically tracking amechanically unattached magnetic probe, the system comprising: (a) amagnetic coil and pole assembly including at least one thin film or thinfoil magnetic pole piece located on a light transmissive substrate andat least one magnetic coil being magnetically coupled to the pole piecefor applying magnetic force to a mechanically unattached probe throughthe pole piece; (b) imaging and tracking optics located proximally tothe pole piece for imaging a sample under test and tracking motion ofthe probe; (c) a position translation stage being mechanically coupledto a sample under test in which the probe resides; and (d) a computercoupled to the magnetic coil and pole assembly, the imaging and trackingoptics, and the position translation stage for receiving positioninformation regarding the probe and the position translation stage andfor producing control signals for moving at least one of the probe andthe position translation stage to maintain position of the probe withina predetermined volume.
 2. The system of claim 1 wherein the magneticcoil and pole assembly includes first and second pole plates, each poleplate having a plurality of pole pieces located thereon.
 3. The systemof claim 2 wherein the pole pieces on the first plate are located in afirst plane and the pole pieces on the second plate are located in asecond plane parallel to the first plane.
 4. The system of claim 3wherein the pole pieces in the first plane include pole tips that formvertices of a equilateral triangle and wherein the pole pieces in thesecond plane include pole tips that form vertices of a secondequilateral triangle located in the second plane.
 5. The system of claim4 wherein the first equilateral triangle is rotated at an angle of 60°with regard to the second equilateral triangle.
 6. The system of claim 1wherein the magnetic coil and pole assembly includes first and secondmagnetic pole pieces.
 7. The system of claim 6 wherein the first andsecond magnetic pole pieces each have a peaked configuration.
 8. Thesystem of claim 6 wherein the computer is adapted to alternatepolarities of the first and second magnetic pole pieces over time. 9.The system of claim 1 wherein the magnetic coil and pole assemblyincludes at least one magnetic core for providing a low reluctance pathfor magnetic flux.
 10. The system of claim 9 wherein the magnetic corecomprises a ring structure having a plurality of tabs located thereonand a plurality of magnetic coils being wound around the tabs.
 11. Thesystem of claim 1 wherein the imaging and tracking optics include afirst objective lens located on a first side of the magnetic coil andpole assembly and a second objective lens located on a second side ofthe magnetic coil and pole assembly.
 12. The system of claim 11 whereinat least one of the first and second objective lenses has a numericalaperture of at least one.
 13. The system of claim 1 wherein the computeris adapted to simultaneously track and control the motion of the probein three dimensions.
 14. The system of claim 1 wherein the predeterminedvolume comprises a volume in which the imaging and tracking optics cantrack position of the probe.
 15. The system of claim 1 wherein thecomputer is adapted to provide a desired position control signal to thestage to cause the sample under test to move in a desired positionprofile and wherein the computer is adapted to provide a probe positioncontrol signal to the magnetic coil and pole assembly for moving theprobe according to a trajectory opposite that caused by moving thesample under test according to the desired position profile, therebymaintaining the probe within the predetermined volume.
 16. The system ofclaim 1 wherein the computer is adapted to provide a desired forcecontrol signal to the magnetic coil and pole assembly for applying adesired magnetic force profile to the probe and wherein the computer isadapted to provide a position control signal to the stage for causingthe sample under test to move in a trajectory opposite the trajectory ofthe probe during application of the magnetic force profile, therebymaintaining the probe within the predetermined volume.
 17. The system ofclaim 1 wherein the computer is adapted to provide a desired velocitycontrol signal to the stage for causing the sample under test to moveaccording to a desired velocity profile and wherein the computer isadapted to provide a probe velocity control signal to the magnetic coiland pole assembly for causing the probe to move in a trajectory oppositethe trajectory caused by application of the desired velocity profile,thereby maintaining the probe within the predetermined volume.